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Let's solve the equation step by step.

The given equation is:

\[
186 = -3y^3 - 6
\]

### Step 1: Isolate the \(y^3\) term.
First, add 6 to both sides to eliminate the constant term on the right-hand side:

\[
186 + 6 = -3y^3
\]
\[
192 = -3y^3
\]

### Step 2: Solve for \(y^3\).
Next, divide both sides by -3:

\[
y^3 = \frac{192}{-3}
\]
\[
y^3 = -64
\]

### Step 3: Solve for \(y\).
To solve for \(y\), take the cube root of both sides:

\[
y = \sqrt[3]{-64}
\]
\[
y = -4
\]

### Final Answer:
The solution for \(y\) is \(y = -4\).

Let me know if you'd like further clarification or additional details.

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Here are 5 related questions to explore:
1. What is the cube root of positive and negative numbers?
2. How would the solution change if the equation was \(y^2\) instead of \(y^3\)?
3. How do you isolate variables in more complex equations?
4. What are the different methods to solve cubic equations?
5. How does the graph of a cubic function compare to a quadratic function?

**Tip**: Always double-check your calculations after each step to avoid simple errors like misplacing signs or numbers.

Solve for y. Express your answer as an integer or integers or in simplest radical form.

186 = -3y^3 - 6

Learn how to solve the cubic equation 186 = -3y^3 - 6 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving cubic equations and isolating variables. Suitable for students in Grades 8-10.

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